**From:** Ben Goertzel (*ben@goertzel.org*)

**Date:** Mon Mar 29 2004 - 07:25:50 MST

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*> One appealing answer to this question of the prior is to
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*> define the prior probability of a possible universe being
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*> base reality as the inverse of the complexity of its laws of
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*> physics. This could be formalized as P(X) =
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*> n^-K(X) where X is a possible universe, n is the size of the
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*> alphabet of the language of a formal set theory, and K(X) is
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*> length of the shortest definition in this language of a set
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*> isomorphic to X. (Those of you familiar with algorithmic
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*> complexity theory might notice that K(X) is just a
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*> generalization of algorithmic complexity, to sets, and to
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*> non-constructive descriptions. The reason for this
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*> generalization is to
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*> avoid assuming that base reality must be discrete and computable.)
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But of course, using this method, for each formal set theory, you can

only distinguish countably many different possible universes -- even

though some of these may be "uncomputable" according to the

computational model adopted.

*> The lack of a objective criteria for choosing a formal set
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*> theory for this purpose leads me to wonder if perhaps the
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*> choice of a prior is a subjective one, similar to the
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*> "choice" of a supergoal in the presumed absence of objective
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*> morality. In case it is, shouldn't we try to answer this
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*> question before building an SI?
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Clearly, the notion of "base reality" as an objective entity is

ill-formes.

Rather, all we have is "apparently base reality, based on the

perceptions and cognitions of mind M, or of minds in class M."

A mind M-1 with greater capability may be able to detect that M's "base

reality" isn't really a "base reality" at all.

One could surely prove that, for any mind, there are some possible

simulations it could be living in, where it could never detect it was in

a simulation -- yet an abler mind could. This would be yet another

Godel theorem varient.

I agree that there is no way to "objectively" choose a prior over the

space of possible universes. This is essentially the problem at the

heart of the Bayesian approach to induction (in the general, Hume-ean

sense). You need a prior distribution on hypothesis space (in this

case, hypotheses about which universe exists).

One approach that's been discussed on this list a lot is algorithmic

information, the Solomonoff-Levin measure, etc. However, this depends

on the base computational model.

One approach here, following Hume, is to take "human nature" as a base

computational model -- so that prior probability becomes "simplicity to

the human mind." Or, taking a page from Eliezer's notion of

humane-ness, perhaps "simplicity to some sort of idealized collective

human mind." But I don't find this very satisfactory.

I'm happier applying the human intuition for simplicity to the *choice

of computational model*. Hence, I prefer a base computational model

involving very simple computational operations, such as the S and K

combinator.... See e.g.

http://homepages.cwi.nl/~tromp/cl/CL.pdf

for an apparently very-close-to-minimal formulation of universal

computation.

As it happens, this ties in with Novamente AI, since our system uses

combinatory logic as part of its knowledge representation.

-- Ben G

-- Ben G

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